A hot-wire anemometer consists of a 5-mm-long, 5-?m-diameter platinum wire. The probe is operated at constant current of 0.03 amp. The electrical resistivity of platinum is 17 ??-cm at 20°C and increases by 0.385% per °C. (a)If the voltage across the wire is 1.75 volts, determine the velocity of the air flowing across it and the wire temperature if the free-stream air temperature is 20°C. (b)What are the wire temperature and voltage if the air velocity is 10 m/s? Neglect radiation and conduction heat transfer from the wire.

Question

GIVEN
• A hot wire in air
• Wire diameter (D) = 5 m = 5 × 10–6 m
• Wire length (L) 5 mm = 0.005 m
• Current (I) = 0.03 A (constant)
• Electrical resistivity (rel) = 17 W cm = 17 × 10–8 W m at 20°C and increases 0.385% per °C.
• Air temperature (T?) = 20°C FIND
(a) The air velocity (U?) and the wire temperature (Tw) if the voltage across the wire (Vel) =1.75V (b) The wire temperature (Tw) and voltage (Vel) if the air velocity (U?) = 10 m/s ASSUMPTIONS
• Radiative heat transfer is negligible
• Variation of Prandtl number with temperature id negligible
PROPERTIES AND CONSTANTS
Thermal conductivity (k) = 0.0251 W/(m K)
Kinematic viscosity (?) = 15.7 × 10–6 m2/s
Prandtl number (Pr) = 0.71
At 90°C: Pr = 0.71

Answer 1

The electrical resistivity of the wire as a function of temperature is



The electrical resistance of the wire is



(a) The voltage across the wire is given by



Solving for the wire temperature



The rate of convective heat transfer for the wire must equal the electrical power dissipated.



Assuming that 1 < Re < 40, and neglecting variation of Prandtl number,

give the heat transfer coefficient as



(b) The Reynolds number at U? = 10 m/s is



Balancing the rate of heat transfer and electrical power dissipation



COMMENTS

Some heat transfer correlations require that air properties be evaluated at the film temperature. This

type of correlation would make the calculation of velocity from a given voltage much more difficult

since the film temperature changes with the wire temperature. In this case, operation in the constant

temperature mode is much simpler because the film temperature is fixed.